The absolute value of a number is the number or the negative of the number
Example will be shown in the equation below
[tex]\lvert{x}\rvert=\begin{cases}={x} \\ ={-x}\end{cases}[/tex]the value of x will be two ......i will show the first solution now
[tex]\begin{gathered} \lvert{x-4}\rvert+3x=x-2 \\ \lvert{x-4}\rvert=x-2-3x \\ \lvert x-4\rvert=-2-2x \\ x-4=-2-2x \\ x+2x=-2+4 \\ 3x=2 \\ x=\frac{2}{3} \end{gathered}[/tex]the first solution was interpreted using absolute value of a number to be the number
the next solution i will show you now will be interpreted using absolute value of a number to be the negative of the number
[tex]\begin{gathered} \lvert{x-4}\rvert=x-2-3x \\ \lvert{x-4}\rvert=-2x-2 \\ -(x-4)=-2x-2 \\ -x+4=-2x-2 \\ -x+2x=-2-4 \\ x=-6 \end{gathered}[/tex]The final answers are x=-6 , and x=2/3
